Area and Perimeter Calculator

How to use Area and Perimeter Calculator

1. Choose a shape and a unit of length.
2. Enter the dimensions that appear for that shape.
3. For a triangle choose base and height, or three sides to use Heron’s formula.
4. Read the area, perimeter and the formulas used.

Formulas used

Rectangle: area = length × width, perimeter = 2 × (length + width). Square: area = side², perimeter = 4 × side. Circle: area = π r², circumference = 2 π r. Triangle: area = ½ × base × height, or with three sides Heron’s formula, √(s(s − a)(s − b)(s − c)) where s is half the perimeter. Trapezoid: area = ½ (a + b) × height. Parallelogram: area = base × perpendicular height, perimeter = 2 × (base + side). Ellipse: area = π a b.

Worked examples: an 8 by 5 rectangle has area 40 and perimeter 26. A circle of radius 5 has area 78.54 and circumference 31.42. A triangle with sides 3, 4 and 5 has s = 6 and area √(6 × 3 × 2 × 1) = 6.

Practical tips

• Use the perpendicular height, not the slanted side, for parallelograms and triangles.
• Measure all dimensions in the same unit before entering them.
• Add a margin for waste when estimating paint, flooring or fabric from an area.
• Fencing and edging use perimeter; coverings such as paint, turf or tiles use area.
• Convert between units by squaring the length conversion: 1 m² is 10,000 cm², not 100.

Limits

Dimensions must be positive numbers. For a triangle with three sides, the sum of any two must exceed the third. The ellipse perimeter is an approximation, and the square-metre figure uses standard definitions of each unit (such as 1 inch = 0.0254 m). Results are for planning and study, not a substitute for professional measurement. Everything runs privately in your browser. For irregular shapes, split them into rectangles, triangles and circles, calculate each part and add the areas; subtract any cut-outs. Keep in mind that real-world surfaces may be slightly uneven, so treat the answer as a planning figure.

Why use this area and perimeter calculator tool

• Seven shapes. Rectangle, square, triangle, circle, trapezoid, parallelogram and ellipse.
• Unit selector. Choose from millimetres to miles; the area is shown in square units with a square metre equivalent.
• Two triangle methods. Base and height, or three sides with Heron’s formula, which also validates that the triangle can exist.
• Formulas on screen. The relevant formulas are displayed so you can follow or reuse them.

Frequently asked questions

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